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die Dateierweiterung (pl. Dateierweiterungen) / die Dateiendung (pl. Dateiendungen) – the file extension
die Dateinamenserweiterung (pl. Dateinamenserweiterungen) – the filename extension
Another word which was built by combining two: Datei (file) + Erweiterung (extension).
File extensions are a suffix that is appear at the end of a file name.
These are things ranging from .txt for text files, to .jpg, .png, and .gif for image files.
That does not mean that anything that appears after the very last dot in the file name is the extension.
You can also have multiple extensions: For example: .tar.gz, used for a tar archive compressed using gzip.
As it turns out, though, what constitutes a file name really depends on the file system.
Most programs don’t rely on the file name for figuring out how to read the file; the file extension is instead meant for us humans. Computers, or rather, programs, can deduce the file type from its header.
This word for “extensions” is also used for browser extensions. Chrome really calls these “Extensions”, though Firefox uses the term “Add-Ons” instead.
What does it mean, when we say that something (A) is an extension of something else (B)? Or that A extends B?
In the general sense, A enlarges the scope of B, or lengthens it, or stretches it out, making it more than what it originally is.
According to Wiktionary, Erweiterung is derived from the verb erweitern.
Duden says that erweitern, in turn, comes from Middle High German wītern, which means to make broader or wider (weit), which comes from MHG wīt, which really means that something has diverged or parted (auseinandergegangen).
And what about Datei, then? Duden says that it was formed following the pattern of Kartei (file, or index, or index cards), which was originally a brand name. This brand name itself was formed following the pattern of Auskunftei (credit agency), which was coined in 1889 by Hermann von Pfister-Schwaighusen, a military historian and writer.